Simplify the following expression and state the condition under which the simplification is valid. $p = \dfrac{z^2 - 16}{z + 4}$
Answer: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = z$ $ b = \sqrt{16} = 4$ So we can rewrite the expression as: $p = \dfrac{({z} + {4})({z} {-4})} {z + 4} $ We can divide the numerator and denominator by $(z + 4)$ on condition that $z \neq -4$ Therefore $p = z - 4; z \neq -4$